Results 11 to 20 of about 33,546 (278)
Iterated Integrals of Jacobi Polynomials [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2019 Let P(α,β)n be the n-th monic Jacobi polynomial with α,β>−1. Given m numbers ω1,…,ωm∈C∖[−1,1], let Ωm=(ω1,…,ωm) and P(α,β)n,m,Ωm be the m-th iterated integral of (n+m)!n!P(α,β)n normalized by the conditions dkP(α,β)n,m,Ωmdzk(ωm−k)=0, for k=0,1,…,m−1. The main purpose of the paper is to study the algebraic and asymptotic properties of the sequence of ...
Hector Pijeira-Cabrera +1 more
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A Legendre Polynomial Integral [PDF]
Mathematics of Computation, 1979 Let { P n ( x ) } \{ {P_n}(x)\} be the usual Legendre polynomials. The following integral is apparently new. \[ ∫ 0 1 P n ( 2 x
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Computing necessary integrability conditions for planar parametrized homogeneous potentials [PDF]
, 2014 Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally parametrized planar homogeneous potential of homogeneity degree $k\neq -2, 0, 2$. We design an algorithm that computes polynomial \emph{necessary} conditions on the parameters $(\a_1 ...
Bostan, Alin +2 more
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Integrability for Nonlinear Time-Delay Systems [PDF]
, 2016 In this note, the notion of integrability is defined for 1-forms defined in the time-delay context. While in the delay-free case, a set of 1-forms defines a vector space, it is shown that 1-forms computed for time-delay systems have to be viewed as ...
Califano, Claudia +2 more
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Liouvillian Integrability Versus Darboux Polynomials [PDF]
Qualitative Theory of Dynamical Systems, 2016 Agraïments: FEDER/UNAB10-4E-378. The second author is supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. The third author is partially supported by NNSF of China grant number 11271252, by RFDP of Higher Education of China grant number 20110073110054, and by ...
Llibre, Jaume +2 more
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Global attractors for a class of semilinear degenerate parabolic equations
Open Mathematics, 2021 In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity ff satisfying the polynomial growth of arbitrary p−1p-1 order.
Zhu Kaixuan, Xie Yongqin
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Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs [PDF]
, 2005 This paper discusses the algorithms and implementations of three MATHEMATICA packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs.
Baldwin, D., Hereman, W., Sayers, J.
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Absorption of closed strings by giant gravitons
Journal of High Energy Physics, 2019 A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi.
Gaoli Chen +3 more
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Perturbative analysis of the colored Alexander polynomial and KP soliton τ-functions
Nuclear Physics B, 2021 In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of SU(N) Chern-Simons Wilson loops, while the limit is N→0.
V. Mishnyakov, A. Sleptsov
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Generalized Ellipsoidal and Sphero-Conal Harmonics [PDF]
, 2006 Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lame polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl ...
Volkmer, Hans
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